Is superintelligence a function of strength or a category?
I’ll have a stab at this. 

Cognitive performance in narrow domains is determined by competency, efficiency and speed. Take calculating numbers, extremely narrow domain but compared to humans the ability of a calculator to calculate numbers exceeds normal human performance, it is much competent in terms of speed. In a bit broader domain, AlphaGo has defeated Go players, which is more difficult than chess, and requires intuition. In fact, there is an instance where the AlphaGo makes a long-term move that was previously unimagined. In all domains however Humans are well rounded, therefore Human Intelligence is called general intelligence. An AlphaGo or Calculator cannot speak eloquently or make music, but AIs are gaining pace in these areas too.

I agree with @nbro that Bostrom wants to keep the interpretation of Superintelligence open. But if there is a rough category, these are- 


ANI- Artificial Narrow Intelligence
AGI- Artificial General Intelligence: Where the AI’s performance is at par with humans. After AGI, it quickly takes off to SI.
SI- Superintelligence: Superintelligence is beyond our imagination, we have not figured out yet what will a SI do, think or want.


While these categories are discrete, the functions of strength are not. I’d say they are rather discrete to continuous, because if you look at the computing power plots that follow Moore’s Law, a similar exponential graph can be drawn for AI’s performance towards general intelligence. In that graph, it seems the AI’s performance starts with discrete performance points, and then as it takes off, it becomes continuous.

This is why the term Singularity is often associated with Superintelligence. I hope this answers your question.